Universität zu Köln

Schmoll, Philipp, Singh, Sukhbinder, Rizzi, Matteo ORCID: 0000-0002-8283-1005 and Orus, Roman ORCID: 0000-0002-4496-8115 (2020). A programming guide for tensor networks with global SU(2) symmetry. Ann. Phys., 419. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE. ISSN 1096-035X

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Abstract

This paper is a manual with tips and tricks for programming tensor network algorithms with global SU(2) symmetry. We focus on practical details that are many times overlooked when it comes to implementing the basic building blocks of codes, such as useful data structures to store the tensors, practical ways of manipulating them, and adapting typical functions for symmetric tensors. Here we do not restrict ourselves to any specific tensor network method, but keep always in mind that the implementation should scale well for simulations of higher-dimensional systems using, e.g., Projected Entangled Pair States, where tensors with many indices may show up. To this end, the structural tensors (or intertwiners) that arise in the usual decomposition of SU(2)-symmetric tensors are never explicitly stored throughout the simulation. Instead, we store and manipulate the corresponding fusion trees - an algebraic specification of the symmetry constraints on the tensor - in order to implement basic SU(2)-symmetric tensor operations. This fusion tree approach is readily extensible to anyonic systems, as we demonstrate for a chain of Fibonacci anyons. (C) 2020 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Schmoll, Philipp UNSPECIFIED UNSPECIFIED UNSPECIFIED Singh, Sukhbinder UNSPECIFIED UNSPECIFIED UNSPECIFIED Rizzi, Matteo UNSPECIFIED orcid.org/0000-0002-8283-1005 UNSPECIFIED Orus, Roman UNSPECIFIED orcid.org/0000-0002-4496-8115 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-325191
DOI:	10.1016/j.aop.2020.168232
Journal or Publication Title:	Ann. Phys.
Volume:	419
Date:	2020
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE
Place of Publication:	SAN DIEGO
ISSN:	1096-035X
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language MATRIX RENORMALIZATION-GROUP; QUANTUM; STATES Multiple languages Physics, Multidisciplinary Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/32519